To determine how many miles Ray can drive on 1 gallon of gas, follow these steps:
1. Identify the amount of gas used: Ray uses [tex]\(\frac{1}{4}\)[/tex] of a gallon of gasoline.
2. Identify the distance driven: Ray drives a distance of [tex]\(5 \frac{1}{2}\)[/tex] miles.
3. Convert the mixed number to an improper fraction:
[tex]\[
5 \frac{1}{2} = \frac{11}{2}
\][/tex]
Thus, Ray drives [tex]\(\frac{11}{2}\)[/tex] miles.
4. Calculate the miles per gallon:
To find out how many miles Ray can drive on 1 gallon, we need to divide the distance driven by the amount of gas used:
[tex]\[
\text{Miles per gallon} = \frac{\frac{11}{2}}{\frac{1}{4}}
\][/tex]
5. Perform the division:
To divide by a fraction, multiply by its reciprocal. The reciprocal of [tex]\(\frac{1}{4}\)[/tex] is 4:
[tex]\[
\frac{\frac{11}{2}}{\frac{1}{4}} = \frac{11}{2} \times 4 = \frac{11 \times 4}{2} = \frac{44}{2} = 22
\][/tex]
Therefore, Ray can drive 22 miles on 1 gallon of gas.
Ray can drive [tex]\(\boxed{22}\)[/tex] miles on 1 gallon of gas.
